Reinstalling software and configuring settings on a new computer is a pain. After my latest hard drive failure set the stage for yet another round of download-extract-install and configuration file twiddling, it was time to overhaul my approach. "Enough is enough!"

This post walks through

how to back up and automate the installation and configuration process

Two microphones are placed in a room where two conversations are taking place simultaneously. Given these two recordings, can one “remix” them in some prescribed way to isolate the individual conversations? Yes! In this post, we review one simple approach to solving this type of problem, Independent Component Analysis (ICA). We share an ipython document implementing ICA and link to a youtube video illustrating its application to audio de-mixing.

In this post, we review two facts about maximum-likelihood estimators: 1) They are consistent, meaning that they converge to the correct values given a large number of samples, $N$, and 2) They satisfy the Cramer-Rao lower bound for unbiased parameter estimates in this same limit — that is, they have the lowest possible variance of any unbiased estimator, in the $N\gg 1$ limit.

We review the two essentials of principal component analysis (“PCA”): 1) The principal components of a set of data points are the eigenvectors of the correlation matrix of these points in feature space. 2) Projecting the data onto the subspace spanned by the first $k$ of these — listed in descending eigenvalue order — provides the best possible $k$-dimensional approximation to the data, in the sense of captured variance.

NBA is back this Tuesday! The dashboard and weekly predictions are now live*, once again. These will each be updated daily, with game winner predictions, hypothetical who-would-beat-whom daily matchup predictions, and more. For a discussion on how we make our predictions, see our first post on this topic. Note that our approach does not make use of any bookie predictions (unlike many other sites), and so provide an independent look on the game.

This season, we hope to crack 70% accuracy!

* Note that we have left up last season’s completed games results, for review purposes. Once every team has played one game, we’ll switch it over to the current season’s results.

“SVMs are among the best (and many believe are indeed the best) ‘off-the-shelf’ supervised learning algorithms.”

Professor Ng covers SVMs in his excellent Machine Learning MOOC, a gateway for many into the realm of data science, but leaves out some details, motivating us to put together some notes here to answer the question:

Here, we review parameter regularization, which is a method for improving regression models through the penalization of non-zero parameter estimates. Why is this effective? Biasing parameters towards zero will (of course!) unfavorably bias a model, but it will also reduce its variance. At times the latter effect can win out, resulting in a net reduction in generalization error. We also review Bayesian regressions — in effect, these generalize the regularization approach, biasing model parameters to any specified prior estimates, not necessarily zero.

Pandas is also a high performance library, with much of its code written in Cython or C. Unfortunately, Pandas can have a bit of a steep learning curve — In this post, I’ll cover some introductory tips and tricks to help one get started with this excellent package.

Notes:

This post was partially inspired by Tom Augspurger’s Pandas tutorial, which has a youtube video that can be viewed along side it. We also suggest some other excellent resource materials — where relevant — below.

The notebook we use below can be downloaded from our github page. Feel free to grab it and follow along.

Let $a_1, a_2, \ldots$ be an infinite set of non-negative samples taken from a distribution $P_0(a)$, and write
$$\tag{1} \label{problem}
S = 1 + a_1 + a_1 a_2 + a_1 a_2 a_3 + \ldots.
$$
Notice that if the $a_i$ were all the same, $S$ would be a regular geometric series, with value $S = \frac{1}{1-a}$. How will the introduction of $a_i$ randomness change this sum? Will $S$ necessarily converge? How is $S$ distributed? In this post, we discuss some simple techniques to answer these questions.